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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank System of circles

  • question_answer
    If the circles \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]and \[{{x}^{2}}+{{y}^{2}}-2gx+{{g}^{2}}-{{b}^{2}}=0\] touch each other externally, then                                   

    A)            \[g=ab\]                                    

    B)            \[{{g}^{2}}={{a}^{2}}+{{b}^{2}}\]

    C)            \[{{g}^{2}}=ab\]                 

    D)            \[g=a+b\]

    Correct Answer: D

    Solution :

               According to the condition,                    \[\sqrt{{{(g-0)}^{2}}+{{(0-0)}^{2}}}=a+b\Rightarrow g=a+b\].


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